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I Help with Anti-Relativity activist

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  1. Nov 17, 2016 #1
    I’m looking for feedback with respect to an SR “paradox”. I’ve gotten myself into a dialog with an Anti-Relativity activist. I know I’ll hate myself in the morning but I thought I would at least make an attempt at explaining this “paradox”.

    You may be familiar with it. It goes like this.

    There is a spaceship traveling at some relativistic horizontal velocity with respect to Earth. In the spaceship is a pulse beacon positioned some distance above a long vertical pipe. At the bottom of the pipe is a light sensor wired to an explosive. From the reference frame of the spaceship, when the pulse beacon flashes, it will create a spherical light wave front that expands at speed c. Some of the light will travel directly down into the pipe triggering the explosion. The file Ref_Frame_Space.gif is intended to show this arrangement (without the walls of the spaceship). I am using a faceted circle for the wave front to make it obvious that a specific part of the wave front enters the top of the pipe and travels to the bottom without needing to go through the walls.


    Now consider the situation from reference frame Earth. The spaceship, pulse beacon and pipe are all moving horizontally. The beacon and pipe remain vertically aligned. Now, when the beacon flashes, from the point of view of Earth, the expanding wave front is at rest with respect to the Earth. It is centered at the location of the beacon at the time of the flash. The file Ref_Frame_Earth.gif is intended to show this arrangement. Note again that a specific facet of the wave front enters the top of the pipe and travels to the bottom without needing to go through the walls, just not the same facet as before. I’ve varied the elevation of the pulse beacon and I always get some part of the wave front making it down the pipe, just different parts.


    Anybody know how to run the gif files? They don't seem to run for me.

    So, two questions:

    1. Are the gif files consistent with relativistic physics?
    2. Assuming they are, what are my chances that I can persuade an SR skeptic with them?
     

    Attached Files:

    Last edited: Nov 17, 2016
  2. jcsd
  3. Nov 17, 2016 #2

    Ibix

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    If you track light rays, you'll find that angular aberration means that it is the same photon going down the pipe. The phenomenon is essentially the same as raindrops falling straight down a pipe, but making a sloped streak on the window of a moving car.

    Your chances of persuading someone who is convinced that relativity is wrong that it is not are pretty much zero in my experience. If you present maths you're a mathemagician. If you present a diagram or description it's not rigorous and you're just spouting dogma. Good luck, though...
     
  4. Nov 17, 2016 #3

    PeterDonis

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    One possible way of describing the misconception involved in not taking aberration into account is this: since the speed of light is the same in all inertial frames in SR, it is natural (but wrong) to assume that a Lorentz transformation has no effect on the direction of light rays. But that assumption is false; a Lorentz transformation does affect the direction of light rays, and this effect is called aberration, as Ibix says.
     
  5. Nov 17, 2016 #4
    Oh. I may be seeing the light at the end of the tunnel.

    Before I read the PeterDonis post, I wrote (but had not yet posted) this reply to Ibix.

    With regard to Ibix “raindrop” comment, this is where I start to have problems. I understand how to transform the position and velocity of objects with mass when switching reference frames. But light doesn’t follow those rules, does it?

    For instance:

    Suppose a raindrop exits the bottom of a leaking bucket at .99c and falls through a vertical pipe positioned somewhere directly below the bucket. If I switch reference frames to one that has horizontal velocity .5c with respect to the pipe, in the new reference frame the bucket, raindrop and pipe will all have a horizontal component to their velocity of -.5c. The raindrop will lose enough of the vertical component to its velocity to make sure its total magnitude is less than c and also make sure the angle of its travel intersects and passes through the pipe. This much I know. I do these kinds of calculations in my 3D computer program a lot.

    But I’m stuck because light does not transform like matter.

    Suppose a light ray at the south pole of an expanding light sphere passes through a vertical pipe positioned somewhere directly below the light source. The light ray has only vertical velocity. If I again switch reference frames to one that has horizontal velocity .5c with respect to the pipe, in the new reference frame the pipe will again have a horizontal component to its velocity of -.5c. But not the light ray. In the new reference frame I must consider the center of the light sphere to again be at rest which means the ray at the south pole must still have only vertical velocity. If that ray acquires any horizontal velocity, the other rays must also and the center of light sphere will be moving/distorting with respect to the new reference frame. And that’s not supposed to happen. I don’t understand how the ray at the south pole can go through the pipe when analyzed in the new reference frame.

    Am I repeating the same misconception about which you guys are writing?
     
  6. Nov 17, 2016 #5
    But it won't be "the ray at the south pole" that will get through our vertical pipe. The ray at the south pole in the old frame of reference won't be at the south pole in the new one.
     
  7. Nov 17, 2016 #6
    If it’s always darkest before the dawn, I am definitely near dawn.

    Just to clarify, I understand that I need to take aberration into account if I have a continuous stream of light whose source is moving with respect to me. But I’m trying to model a light pulse, one of very short duration, as a thin expanding spherical shell of light. If the light ray at the south pole of the shell as identified in one reference frame is not at the south pole with respect to another reference frame, how do I transform the locations of the light rays from one reference frame to another? I know I have to end up with another sphere. Different radius is OK but changing the radius won’t change the location/direction of the south pole ray. Rotation?
     
  8. Nov 17, 2016 #7

    Ibix

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    Think of your pipe with a laser pointing down it. Emit a pulse from the laser - it goes down the pipe.

    Now think how that looks from a moving frame. The pipe is moving perpendicular to its length. The light pulse must also have motion in that direction to be going down the pipe. So the pulse cannot be travelling straight down in this frame.

    This is true in Newtonian physics as well - raindrops falling straight down in the road frame are falling diagonally in a moving car's rest frame. But the raindrops are moving faster in the car's frame. At relativistic speeds, though, time dilation and length contraction come into play. And for light, they make the speed constant.
     
  9. Nov 17, 2016 #8

    phinds

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    Well, there's your problem right there. Science deniers are not interested in facts so you are doing what is known in the military as "pissing up a rope".

    To understand this for yourself is a good thing but arguing with a science denier ... ?
     
  10. Nov 17, 2016 #9
    Everybody tells me that. And I keep doing it anyway. That's a form of denial too I guess.
    On top of that the denier exposed a serious gap in my understanding of SR. Now I have to post back to him that I have no explanation for him.
    And I don't understand the explanations be given to me.

    Could be worse. Could be raining.
     
  11. Nov 17, 2016 #10

    Ibix

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    You can just use the Lorentz transforms. The pipe is at x=0, -1>y>-2. A light pulse is emitted at the origin at t=0; its position in general is x=0, y=-ct. Use the LTs to show that the pulse enters the pipe in any frame and moves at c in any frame.
     
  12. Nov 17, 2016 #11

    pervect

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    These appears to be screen captures of some program output. You can't "run" the images, you'd need the executable. I can't tell what program they are outputs of.

    I can't tell from the information provided. In the moving frame, if they were correct, I'd briefely describe what should be drawn as a moving tube that remains vertical, and a slanted (aberrated) light ray moving on a diagonal which stays inside the moving tube. This is basically the same answer that other posters have given. I don't quite follow what claims are being made by the "anti-relativisit activist".

    I'd guess not much chance, to be honest. If someone is interested in debating, in my experience they're not actually listening or trying to understand. There may be other reasons you'd want to reply or discuss the problem, other than a very tiny chance of convincing your opponent, you might want to think about what they could be. If your sole and only goal is convincing the "anti-relativist activist", chances are you'll be dissapointed.
     
  13. Nov 17, 2016 #12
    Yeah, the rays will get a little boost in the direction of the horizontal movement (of the source of light), but since the magnitude of the speed of each ray should stay the same (speed of light) their vertical components will change too, and the effect will be that of a rotation (in the direction of movement). The south ray won't be the south ray anymore. I'm not sure what you mean by "different radius", the sphere is still expanding at the speed of light in every (inertial) frame of reference.
    If you draw the picture of the resulting "sphere of rays" you'll also notice an additional effect - if we have a perfectly isotropic sphere of light in the original frame (where the source of light is initially at rest), in the "moving" frame of reference the sphere is not isotropic (in terms of rays distribution), there is more light on one side (in the direction of the movement of the source of light), than on the other side.
    You can also notice that since the tube is moving too (in the "moving" FoF), by the time the expanding sphere of light reaches it, the tube won't be directly below the center of the sphere (which, since the speed of light is constant, is at rest even in the "moving" FoF) of light, and the ray that will reach the tube will be slanted (the old "south pole" ray). Since it's slanted, it has lower vertical speed, and it will take it more time to reach the tube, than it takes him in the original FoF (where the tube is at rest). Time dilation at work.
     
  14. Nov 18, 2016 #13

    vanhees71

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    As usual, a formula says more than 1000 words ;-)). Take a plane electromagnetic wave ##\propto \cos(\omega t-\vec{k} \cdot x)=\cos (k \cdot x)## with the four-vector ##(k^{\mu})=(\omega/c,\vec{k})=(|\vec{k}|,\vec{k})##. The four-wave vector transforms as any other four-vector under Lorentz transformations
    $$k^{\prime \mu}={\Lambda^{\mu}}_{\nu} k^{\nu},$$
    and for a Lorentz boost it's easy to see that ##\vec{k}'## is in a different direction than ##\vec{k}##, and that's the aberration of light.
     
  15. Nov 18, 2016 #14
    This is progress. I didn't think I could use the LT because it was a light pulse and I thought the LT was only for objects moving at speeds < c.

    As I look down the other posts I see Dragon27 and vanhees71 also refer to transforming using LT. I thought if I tried that, I would no longer end up with a spherical wavefront. So now I will try it and see what I get. I have a 3D Lorentz Transform matrix. This may take a while.
     
  16. Nov 18, 2016 #15
    I created two animated gifs from two sets of screen captures. I verified the gifs run on my computer. I thought if I just inserted the gifs into the post, they would be runable inside the post. But as you noticed they are not. Is there a special rule/procedure I need to follow?
     
  17. Nov 18, 2016 #16

    Ibix

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    You can't transform into a frame where the light pulse is at rest, no, because there's no such thing. But that's not what you're trying to do here. You know the coordinates of the light pulse in one frame (I wrote them down), and you can use the Lorentz transforms to get the coordinates in another one which is moving at less than c - which is what you were talking about.

    If it makes you feel more comfortable, scatter light sensors throughout space, at rest with respect to your pipe. Think of transforming the coordinates of the events where they light up.

    This sounds more complex than I expect. You just need the transforms for motion in the x-direction - it's the motion of the observer that matters, and if you lay your pipe in the y-direction then your observer can move in the x-direction.
     
  18. Nov 18, 2016 #17

    pervect

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    Here is a concise description of the math needed for the simple case under consideration, using somewhat less advanced notation than that in vanhees71's post.

    The diagram is represented mathematically by a collection of points. In system S, where the tube is at rest, we will represent each point p by the coordinates (t,x,y). Note that specifying the tube will require an infinite number of points. The light pulse, though, assuming it's instantaneously short, will require the specification of only one point p.

    Special relativity gives us a mathematical rule for converting any point p from system S, where the tube is at rest, to apoint p' in system S', where the tube is moving. In S', we will denote the coordinates of point p' as (t', x', y').

    The mathematical formula that maps point from S to S' is called the "Lorentz Transform". You can find the required equations in any book on special relativity, or on the www, for instance the wikipedia https://en.wikipedia.org/w/index.php?title=Lorentz_transformation&oldid=747253773

    Rather than give the most general expression for the Lorentz transform, I'll give the expression for a simple case. In this simple case, system S' is moving relative to sytem S in the x direction with some velocity v.

    If system S' is moving in the x direction, we can follow the wiki formula that gives us the map from the coordinates of point p in s , i.e (t,x,y,z) to the point p' in S', i.e. (t', x', y').

    $$t' = \gamma(t - vx/c^2) \quad x' = \gamma(x -vt) \quad y'=y$$

    We've introduced the symbol ##\gamma## which is given by the formula ##\gamma = 1 / \sqrt{1-v^2/c^2}##

    I really couldn't say if the program you're pasting the output of follows these rules, or not.
     
  19. Nov 18, 2016 #18

    phinds

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    Yes. Post them on a web server somewhere that has the requisite server software and then post a link to them. PF does not have that software.
     
  20. Nov 18, 2016 #19

    DrGreg

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    It is possible to upload animated GIFs to this forum: see, for example, https://www.physicsforums.com/threads/how-does-light-slide-sideways.804112/page-2#post-5048516. But I posted that some time ago and I can't remember exactly how I did it.:frown:
     
  21. Nov 18, 2016 #20

    OCR

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    I thought so too... here's one from Wikipedia that I just downloaded and saved to "My Pictures"...

    Nonsymmetric_velocity_time_dilation.gif

    I actually downloaded it from here ...

    This is the actual file location, though ...

    Yeah, it seems to be, here's the URL to the one you uploaded, DrGreg...

    https://www.physicsforums.com/attachments/bounce-in-a-moving-train-gif.80718/

    Here's the URL to one that MikeLizzi uploaded...

    https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/92/92117-7f7b77c2be0b0763124373671bf010fc.jpg [Broken]

    Looks like it's a jpg...

    And, how do you get an animated screen capture ? ... :oldconfused:

    PS: And, this is the new ?... URL to the one from wiki that I just uploaded...

    https://www.physicsforums.com/attachments/nonsymmetric_velocity_time_dilation-gif.109103/
     
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